System and method for temporal sparse promoting imaging of cardiac activation

ABSTRACT

A system and method for cardiac activation imaging includes non-invasively or minimally invasively acquiring data about an electrical activation of a heart of a subject using at least one sensor. An activation image of the heart of the subject is reconstructed using a weighted sparse constrained reconstruction.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is based on, claims priority to, and incorporatesherein by reference U.S. Provisional Patent Application No. 61/905,451,filed Nov. 18, 2013, and entitled, “SYSTEM AND METHOD FOR TEMPORALSPARSE PROMOTING IMAGING OF CARDIAC ELECTRICAL ACTIVATION.”

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH

This invention was made with government support under HL080093-01A2awarded by the National Institutes of Heath. The government has certainrights in the invention.

BACKGROUND

The present disclosure relates to systems and methods for acquiringmedical data and, more particularly, to imaging of cardiac activation.

Cardiac disease is a significant challenge to public health and aleading killer in the United States, costing more than 270 billiondollars annually in the United States alone. Each year, about 400,000sudden cardiac deaths are reported in the United States while a majorportion of them are induced by ventricular arrhythmias. In clinicalpractice, anti-arrhythmic medications are usually administered tosuppress the life-threatening syndromes. For the medically refractorycases, catheter ablation has become a standard procedure to eliminatethe arrhythmias. The success of such catheter ablation relies oninformation regarding the arrhythmogenesis. Contact and non-contactintra-cardiac mapping technologies have been employed to guide catheterablative procedures. However, limited by its invasive nature, theseapproaches are often time consuming and can only map the cardiacelectrical activity on the endocardium of a single or only partialventricular chamber. Therefore, there is a clinical need to developnon-invasive imaging modalities that can image the cardiac electricalactivity throughout the 3D myocardial volume. Such clinical informationwill improve the effectiveness and efficiency of catheter ablationtreatment and also help elucidate the mechanisms of ventriculararrhythmias.

Efforts have been made pursuing noninvasive approaches of mappingcardiac electrical activity by solving the inverse problem ofelectrocardiography (ECG). Moving dipole localization techniques seek torepresent whole heart electrical activity with either one or severalmoving dipoles. Epicardial imaging techniques expand the solution spacefrom few dipole sources to potential distributions over the epicardialsurface. Heart surface activation imaging, alternatively, directlysolves myocardial activation time on the heart surfaces based on aphysiological model. These methods have been shown to providepotentially valuable information noninvasively, although they estimatecardiac electrical activity over the epicardium or the heart surfaces(including epicardial and endocardial surfaces) instead of over the 3Dmyocardium.

Over the past decade, cardiac electrical imaging approaches consideringthe whole myocardium have been pursued. Physiological model basedmethods incorporate a priori knowledge based physiological model intoinverse solutions to solve the ECG inverse problem. Recently, aphysical-model based 3D Cardiac Electrical Imaging (3DCEI) approach hasbeen developed and validated on various animal models, such as rabbitsand canines, in which good concordance was observed with 3Dintra-cardiac mapping results. However, the minimum energy basedWeighted Minimum Norm (WMN) method employed by 3DCEI limits thespatial-temporal resolution and robustness against non-Gaussiandisturbance such as geometrical modeling error and electroderegistration error, which can be introduced in realistic scenarios dueto limited raw data quality. The electrophysiology-irrelevant minimumenergy constraints imposed may become dominant in reconstruction,leading to a smoothed and distorted imaged activation sequence.

Therefore, the need remains for new and improved non-invasive imagingmodalities that can image the cardiac electrical activity throughout the3D myocardial volume.

Similarly, efforts have been pursued for minimally invasive cardiacimaging using recordings made by catheter. However, there is a need toimprove catheter based activation imaging throughout the 3D myocardialvolume.

In parallel to electrocardiographic imaging, efforts have also been madeto image cardiac electrical activity from magnetocardiographicrecordings made out of torso. However, high resolution activationimaging from magnetocardiography (MCG) has been challenging.

SUMMARY

The present invention overcomes the aforementioned drawbacks byproviding systems and methods for cardiac electrical sparse imaging(CESI), which is a new electrical imaging technique. CESI provides a 4Dinverse problem formulation to incorporate sparse property of cardiacelectrical activity to preserve the temporal resolution and detailedactivation information for improved imaging accuracy and robustness incomparison with traditional linear inverse solutions. CESI reconstructscardiac electrical activation in a weighted group sparse promotingstrategy based on a physical model to exploit sparse properties ofelectrical activity and, therefore, improve the spatial-temporalresolution and the robustness in imaging the cardiac activity.

In accordance with one aspect of the invention, a system is disclosedfor cardiac activation imaging. The system includes at least one dataacquisition device configured to acquire data about an electricalactivation of a heart of a subject and a processor. The processor isconfigured to receive the data acquired by the at least one dataacquisition device and generate a cardiac electrical activation image byreconstructing an activation image of the heart of the subject using aweighted sparse constrained reconstruction.

In accordance with another aspect of the invention, a method isdisclosed for acquisition of cardiac activation imaging data. The methodincludes acquiring data about an electrical activation of a heart of asubject using at least one sensor and reconstructing an activation imageof the heart of the subject using a weighted sparse constrainedreconstruction. The method also includes displaying the activation imageof the heart.

In accordance with another aspect of the invention, a system isdisclosed for minimally invasive imaging of cardiac activation from datacollected by a catheter. The system includes acquireelectrophysiological data simultaneously or sequentially from acatheter, and anatomic information, and reconstruct an activation imageof the heart of the subject using a weighted sparse constraintedreconstruction, and display together with cardiac anatomy or cathetermapping results.

In accordance with another aspect of the invention, a system isdisclosed for non-invasive imaging of cardiac activation from datacollected by a MCG recording device. The system includes acquire MCGdata, and anatomic information, and reconstruct an activation image ofthe heart of the subject using a weighted sparse constraintedreconstruction, and display together with cardiac anatomy or othercardiac mapping results.

The foregoing and other aspects and advantages of the invention willappear from the following description. In the description, reference ismade to the accompanying drawings which form a part hereof, and in whichthere is shown by way of illustration a preferred embodiment of theinvention. Such embodiment does not necessarily represent the full scopeof the invention, however, and reference is made therefore to the claimsand herein for interpreting the scope of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic illustration of a system in accordance with thepresent invention.

FIG. 2A is a graph showing transmural electricity.

FIG. 2B is an illustration of a depolarization state at an instant, τ.

FIG. 3 illustrates an experimental paradigm of animal experiment, whereA shows an experimental animal, B shows a multi-channel body surfaceECG, C shows geometrical information from CT scan, D shows aintra-cardiac transmural recording simultaneously done with body surfaceECG collection, E shows an activation sequence imaged with WMN method, Fshows an activation sequence from the CESI method, and G shows ameasured activation sequence from intracardiac transmural recording.

FIG. 4 is a set of graphs showing a comparison of imaging statisticsbetween the CESI method and the WMN method for 12 site single pacingsimulations.

FIGS. 5A through 5D provide sets of images that compare between asimulated activation sequence and an imaged activation sequence from theCESI method and the WMN method.

FIGS. 6A-6E provide sets of images that compare imaged results from theCESI method and the WMN method studies from pacing simulation withvarious modeling errors.

FIG. 7 is a set of graphs providing a comparison of the averagedstatistics between the CESI method and the WMN method on single sitepacing simulations with modeling errors on 12 single pacing sites.

FIGS. 8A and 8B provide sets of graphs that compare examples andstatistics between studies using the CESI method and the WMN method inrabbit pacing experiment.

FIG. 9 is a set of graphs providing summarized statistics of activationimaging using the CESI method compared with the WMN method during pacingin rabbit.

FIG. 10 is a schematic illustration of another system in accordance withthe present invention.

DETAILED DESCRIPTION

Non-invasive approaches to image cardiac activation can provideimportant information besides the traditional intra-cardiac mapping toaid ablation therapy and cardiovascular research. The present inventionprovides a system and method for cardiac electrical sparse imaging(CESI). CESI can image the cardiac electrical activation throughout themyocardium, preserving full temporal resolution and at high spatialresolution. As will be described, CESI can employ a 4D inverse problemformulation to incorporate sparse property of cardiac electricalactivity to preserve the temporal resolution and detailed activationinformation for improved imaging accuracy and robustness in comparisonwith traditional linear inverse solutions. CESI reconstructs cardiacelectrical activation in a weighted group sparse promoting strategybased on a physical model to exploit sparse properties of electricalactivity on myocardium and, therefore, improve the spatial-temporalresolution and the robustness in imaging the cardiac electrical activitythree dimensionally. As will be described, the imaged results werevalidated by simultaneous intra-cardiac transmural recording andcompared with those from traditional 3D imaging approaches representedby weighted minimum norm (WMN) method as partial evaluation.

In particular, referring to FIG. 1, a system in accordance with thepresent invention is illustrated. The system 10 includes at least onesystem to acquire information from a patient 12. For example, an ECGsystem 13 having at least one electrode or sensor may be configured tobe placed on an external surface of the patient 12 to provide ECGrecordings 14. Also, a medical imaging system 15 may be employed toacquire medical imaging data from the patient 12 to generate structuralor anatomical imaging data. The ECG recordings 14 can be used togenerate body surface ECG reports 18. The body surface ECG reports 18can be processed further to generate a body surface potential map (BSPM)20. As will be described, the recorded ECG data 14, regardless of theparticular electrode or sensor design or configuration used foracquisition, can be transformed to BSPMs and, used to create CESIactivation images 24, which may be activation images of the heart of thepatient 12 reconstructed using a weighted sparse constrainedreconstruction.

To do so, the structural imaging data 16 is used to create 3D or aseries of 2D image slices that contain information about the geometry orunderlying anatomy information 26 of the patient 12. To this end, themedical imaging system may include a computed tomography (CT) imagingsystem, a magnetic resonance imaging (MRI) system, or a variety of otherimaging modalities capable of providing geometric information about theanatomy of the patient 12. The geometry or underlying anatomyinformation 26 is used in a modeling process 28 to generate a geometricmodel of the subject 12 that describes the patient's anatomy usingboundary element method (BEM) 30. This geometric model is combined withthe data from the BSPMs 22, using a processor 32 to implement a sparsereconstruction process that will be described, to generate the 3Dactivation images 24. As will be further described, the above-describedprocessing 20 and modeling 28 may also be performed in the processor 32,or may be performed using other processors.

As will be described, inverse solutions have been investigated forcardiac electrical imaging, such as using equivalent current density(ECD) models. However, these investigations did not incorporate anyphysiological knowledge and reconstruct each timeframe independently,leading to a temporal smoothing effect and losing temporal resolutionand details. As will be described, sparse constraints can be applied toinverse problem formulation in order to produce solutions with sparsefeatures. However, simple sparse constraints are sensitive to noise andstruggle to present the temporal dynamics properly. The CESI methodsdescribed herein, provide dipole-wise temporal weighted sparsereconstructing strategy that can be implemented by a processor to createthe CESI activation images 24.

Trans-Membrane Potentials (TMPs) and Temporal Sparse Property in SpatialDerivative

When a myocardial cell is activated, the TMP has a transient rise fromthe −90 mV resting state to the plateau potential at around 0 mV.Regardless of individual variations in the resting or plateau potential,the impulse of transmembrane current flow, corresponding to the temporalderivative of TMP, can indicate the time of cell activation by sharppeaks while during the remainder of the cardiac cycle, the cell isnearly electrically silent. In accordance with the present invention,this can be reviewed as a sparse property of the cardiac electricalactivity in the temporal domain that can potentially be exploited forenhancement in imaging.

The spatial derivative of the TMP, equivalently, can be an indicator ofactivation propagation throughout the spatial domain of the myocardium.Activation propagates through the heart and generates a wave frontbetween the resting and the depolarized myocardial tissue. For eachmyocardial cell, the TMP time course consists of two distinguishedphases and a rapid transition between them. For example, FIG. 2A is agraph showing transmural electricity and FIG. 2B is an illustration of adepolarization state at an instant, τ. Thus, together FIGS. 2A and 2Billustrate the temporal sparse property of cardiac electrical activity.The rapid potential shift from the polarized −90 mV to the depolarized 0mV during propagation can generate an excitation wave front as well as aspike in current density for the myocardium at the wave front. On theother hand, the current density during the relatively stable potentialin both resting and plateau stage is much smaller and can be consideredas electrically silent compared with the spike. Therefore, the currentdensity in each site of the myocardium can be assumed as a sparsesignal. However, this sparsity can only hold in the temporal domain.Although each myocardial cell in a cardiac cycle is activated only once,a considerably large portion of the heart can possibly be excited at thesame time as excitation propagates. Note that the spatial derivative ofTMP along a certain direction can be directly measured by bipolarrecordings, a well-established mapping technology. As will be described,this realization allowed validation of the performance of the cardiacelectrical imaging results in a rigorous manner.

Equivalent Current Density (ECD) Model & Transfer Function

At location r and time instant t, equivalent current density J_(eq) canbe defined as:

J _(eq)(r, t)=−G _(i)(r)∇Φ_(m)(r, t)   (1);

where G_(i)(r) stands for the intracellular effective conductivitytensor at location r and Φ_(m)(r,t) is the transmembrane potential.

Based on bidomain theory and distributed ECD model, the discretearchitecture of the myocardial cell can be generalized into a model on amacroscopic continuum where the electrical activity in myocardium can berepresented with two components: intracellular and extracellular domainsdivided by a theoretical membrane. The electrical behavior of assumedquasi-static state electrical field is governed by:

∇·[(G _(i)(r)+G _(e)(r))∇Φ_(n)(r, t)]=∇·{right arrow over (J)} _(eq)(r,t)   (2);

where G_(e)(r) and G_(i)(r) are the intracellular and extracellulareffective conductivity tensors and Φ_(e)(r,t) is the extracellularpotential at location r, time instant t. The differential equation (2),with boundary element model approximation, can be linearized into amatrix-vector transfer function shown as:

{right arrow over (Φ)}=L{right arrow over (J)}  (3);

where L stands for the transfer matrix {right arrow over (Φ)}, {rightarrow over (J)} are vectors of body surface potentials and equivalentcurrent density at the source grid points inside the myocardium,respectively. Matrix L is an M×3N matrix connecting M sensormeasurements and the current density dipole momentums on N myocardialgrid points. On each grid point, 3 momentums are considered inequivalence of a current density vector. Equation (3) represents alinear relation between body surface ECG and equivalent current densityover a number of grid points covering the myocardium at a certain timeinstant. To expand this to the entire time course, equation (3) can bereformed into:

$\begin{matrix}{{\overset{\rightarrow}{\Phi}}_{T} = {L_{T}{\overset{\rightarrow}{J}}_{T}}} & (4) \\{L_{T} = \begin{bmatrix}L & \; & \; & \; \\\; & L & \; & \; \\\; & \; & \ddots & \; \\\; & \; & \; & L\end{bmatrix}} & (5)\end{matrix}$

where L_(T) is a MT×3NT matrix which connects the body surfacepotentials over a period of time, Φ_(T), and the equivalent currentdensity over a period of time J_(T). In equation (4), a transferfunction from the electrical activity on a time course for eachmyocardial voxel to body surface potential for the time window isconstructed. The temporal dynamic of cardiac electrical activity and itssparse property can be described in J_(T) and shown in the reconstructedsolutions provided hereafter.

The matrix-vector equation (3) can be represented as the following whenMCG data is involved:

B=AJ   (3b)

where A stands for the transfer matrix relating cardiac sources J tomagnetic field B; and B,J are vectors of magnetic field produced bycardiac currents out of the torso, and equivalent current density at thesource grid points inside the myocardium, respectively. Matrix A is anM×3N matrix connecting M sensor measurements and the current densitydipole momentums on N myocardial grid points. On each grid point, 3momentums are considered in equivalence of a current density vetor.Equation (3b) represents a linear relation between MCG and equivalentcurrent density over a number of grid points covering the myocardium ata certain time instant. To expand this to the entire time course,equation (3b) can be reformed into:

B_(T)=A_(T)J_(T)   (4b)

Where A_(T) is similar to (5) except L_(T) refers to transfer functionfor electric potential and A_(T) refers to transfer function formagnetic field.

Weighted Sparse Constrained Reconstruction

As presented above, equation (4) formulates a forward problem thatconnects the spatiotemporal dynamics of cardiac electrical activity withthe body surface potential maps (BSPMs). However, the formulated problemis seriously ill-posed and cannot be solved directly. Minimum energybased inverse solutions have been investigated for cardiac electricalimaging. However, the pure physical constraints fail to incorporate anyphysiological knowledge and reconstruct each timeframe independently,leading to a smoothing effect that decreases temporal resolution anddistorts the activation sequence. Sparse constraints can be applied tothe inverse problem formulation in order to produce solutions withsparse features. However, simple sparse constraints are sensitive tonoise and cannot present the temporal dynamics in the heart properly.The present CESI method provides a dipole-wise temporal weighted sparsereconstructing strategy will be applied as:

$\begin{matrix}{{{\hat{J}}_{T} = {{argmin}\left( {{{\overset{\rightarrow}{J}}_{T} - {L_{T}{\overset{\rightarrow}{\Phi}}_{T}}}}_{2}^{2} \right)}};} & (6) \\{{{s.j.{\sum\limits_{t}^{T}{W_{t,i}{{\overset{\rightarrow}{J}}_{t,i}}_{2}^{1}}}} < {\mu \; E_{i}\mspace{14mu} {for}\mspace{14mu} {all}\mspace{14mu} i}};} & (7)\end{matrix}$

where W_(t,i) represents the soft temporal weights of time instant t atlocation grid point i. {right arrow over (J)}_(t,i) stands for thecurrent density vector [J_(x), J_(y), J_(z)] at instant t and myocardialsource grid i. E_(i) represents the estimated energy of ECD along timecourse t at location i. W_(t,i) and E_(i) can be derived by:

$\begin{matrix}{{W_{i,t} = {\exp \left( {{- C_{t,i}}/C_{m\; {ax}}} \right)}};} & (8) \\{{E_{i} = \sqrt{\sum\limits_{T}C_{t,i}^{2}}};} & (9) \\{{J_{w} = {{{argmin}{{{LJ}_{w} - \Phi}}_{2}^{2}} + {{W_{w}J_{w}}}_{2}^{2}}};} & (10)\end{matrix}$

where C_(t,i), is the amplitude of WMN reconstructed current densityJ_(w) at instant t and myocardial source grid i solved with weightedminimum norm method as described in Z. Liu, C. Liu and B. He,“Noninvasive Reconstruction of Three-Dimensional Ventricular ActivationSequence form the Inverse Solution of Distributed Equivalent CurrentDensity,” IEEE Transaction Medical Imaging, vol. 25, pp. 1307-1318,2006, which is incorporated herein by reference in its entirety.C_(max), is the maximum value of C_(i,t) along the time course T at eachlocation i. W_(t,i) is designated to help stabilize the sparse solutionsat the same time evading the smearing effect and distortion a minimumnorm solution may have. When C_(t,i) gets smaller, indicating a smallerlikelihood that the activation may occur, W_(t,i) becomes larger,imposing a larger penalty and the final electrical spikes are lesslikely to be occur at the instant.

All the current density time course from equation (10) may be normalizedso that the total penalty on each site will be approximately same.Therefore, the balanced of each grid point can be kept. The constraintsin equation (7) have a soft guiding effect on the final temporal sparseresults. When the weighted minimum norm is “confident” about thereconstructed result, namely a distinguished peak is reconstructed, thepenalty for disagreeing will be larger. On the other hand, in thesituation where only smoothed waveform or multiple peaks are generateddue to noisy background or modeling error, which is the major source oferror in WMN method, CESI will seek for activation in a larger range andrely more on the information from BSPM and other “confident” results. Inthis way, the merit of WMN can be preserved while the weakness can beavoided. E, on the opposite side of the constraints, is directly linkedto the energy of the weighted minimum norm solutions and the effect ofdistributing lead-field energy can be canceled out.

Note that equation (6) serves as the dominating term in reconstructionwhile equation (8) only bring in minimum norm inverse solutions assecondary guiding information. In contrast to the minimum energy basedconstraints from which most entries in the solution vector can benon-zero to compensate the residual term in equation (6), the sparseconstraints in equation (7) designed in the present method enforceelectrical silence except for the very instant of activation. Therefore,the tendency for loss of temporal resolution and distortion is heavilypenalized by the residual term due to the total absence of electricalactivity in other instants and the information from BSPM can beefficiently reflected in the reconstructed results without compromise toa stronger regularization term as the disturbance from noise or modelingerror become more serious. At the same time, the sensitivity of sparsereconstruction to sensor noise can be overcome by weighting based on theGaussian-noise-robust minimum energy solutions. Instead of a direct L1,the sparse constraints in equation (7) adapt a grouped sparseformulation in which the three momentums in {right arrow over (J)}_(t,i)are considered grouped and only the amplitude of {right arrow over(J)}_(t,i) is sparse and only in the temporal domain. The μ in equation(7) can be determined by a data driven regularization algorithm such asthe L-curve method. Equations (6) to (9) define a convex constrainedproblem and can be solved equivalently using various methods. As anon-limiting example, these can be solved with CVX, a software packagefor specifying and solving convex programs. Activation time, accordingto the peak criterion, may be computed based on CESI imaged electricalactivity and the 3D activation sequence throughout the myocardium isgenerated accordingly.

CESI, with its novel formulation, stressing sparsity in the temporaldomain, incorporates the whole 4D spatiotemporal cardiac dynamics inreconstruction. The temporal dynamic specific sparse formulation isapplied in the imaging of a 4D functional process allowing sparse andnon-sparse properties to cooperate in imaging for a higher accuracy andspatiotemporal resolution. The method does not promote sparsity inspatial domain but only in temporal domain. Thus, the imaging result ofthe present method can better image the spatial cardiac activation in aspatial sparse or non-sparse manner. Due to the temporal sparseconstraints, the spatial area of electrical activation at a specificinstant is mainly determined by the information from the residual termin equation (6). In contrast, as will be demonstrated, the minimum normmethod can only generate a smoothed waveform along the time course andlarge of the myocardium will be electrically active during most of thebeat. Therefore, the effective spatial resolution of CESI is improvedeven with the same source grid resolution by avoiding spatial smoothingeffects. This property in spatiotemporal domain improves the method'scompatibility and performance for both the early phase, where theactivation is sparse, and the later phase, where a major portion of themyocardium is in activation, of the cardiac cycle.

For MCG activation imaging, equation (4b) instead of (4) should be usedand the CESI algorithm can be applied to MCG data.

Computer Simulation

In order to evaluate the performance of the described method on humanapplications in a realistic scenario, a cellular automaton heart modelembedded in a realistic heart-torso volume conductor model was used. Ageneralized cardiac anisotropy was incorporated into the heart model andthe myocardial fiber rotated counterclockwise over 120 degrees from theoutermost layer to the innermost layer. The conduction velocity is 0.8m/s along the fiber and 0.3 m/s transverse. The myocardium consists of atotal of 30,085 cardiac automatons and 4,096 torso surface vertices wereconstructed. Two hundred electrodes were evenly distributed on both thechest and the back in the computer simulation. Pacing simulations onvarious locations were employed, including the basal anterior (BA),basal left wall (BLW), basal right wall (BRW), basal posterior (BP),basal Septum (BS), middle left wall (MLW), middle right wall (MRW),middle anterior (MA), mid-septum (MS), middle posterior (MP), apicalanterior (AA) and Apical posterior (AP). Dual site pacing was alsosimulated in the present study with seven pairs of pacing sites selectedthroughout the ventricle myocardium. One pacing site was fixed at themid lateral RV free wall while the other one gradually moved towards themid left wall. BSPMs were computed by means of the Boundary ElementMethod (BEM) with simulated cardiac electrical sources using thecellular automaton model.

Various kinds of experimental noise and modeling error were consideredto simulate noise-contaminated measurements in a clinical setting. WhiteGaussian noise of different levels (20-80 μV) was utilized as the sensornoise. Noise signal that randomly selected from hospital ECG recordingswith ECG waveform rejected was also used to simulate realistic noisesuch as power line interference, medical device interference andmovement drift. Heart and torso modeling error were also simulated wherethe size of the torso was inflated by 10% and the location of the heartinside was moved 4 mm towards the lung. To simulate the electrodelocalization errors that could occur in the realistic applications, suchas electrode-CT geometrical co-registration, the electrodes were moved1cm upward from its original locations.

Validation in Animal Experiments

To validate the described imaging method, experimental data wascollected in two healthy New Zealand rabbits. In particular, FIG. 3illustrates the experimental setup. In brief, cardiac CT and torso CTwere performed on the experimental rabbits prior to in vivo mapping.About 60 BSPM electrodes were uniformly placed covering the anterior andlateral rabbit. Approximately, 20-25 transmural needles were inserted inthe left and right ventricles of the rabbit after median sternotomy witheach needle carrying 8 bipolar sensors 500 μm distant to each other. Thechest and skin were carefully closed after needle insertion. Bipolarelectrograms were recorded from all electrodes continuously andsimultaneously with body surface ECG mapping. After the recording,electrode needles were replaced with metallic label. CT scans wereperformed on the excised and fixed hearts to obtain precise 3Dlocalization of the transmural electrodes. A Gaussian interpolation wasperformed on the activation time detected from intra-cardiac bipolarrecording according to the CT geometry to generate a 3D measuredactivation map. The rabbit myocardium was tessellated into around 10,000grid points evenly located within the 3D ventricular myocardium. Therewere around 160-200 intra-cardiac bipolar electrodes placed in both theventricles for intra-cardiac mapping. The ventricular activationsequences were imaged from the BSPM and quantitatively compared withthose recorded simultaneously.

Data Analysis

Correlation Coefficient (CC), Relative Error (RE), Localization Error(LE) and Relative Temporal Shrinkage (RTS) were computed for bothcomputer simulation and animal experimental data, as defined below:

${{CC} = \frac{\sum\limits_{i}{\left( {{AT}_{i} - {MT}_{i}} \right) \cdot \left( {{ATA}_{i} - {MT}_{i}} \right)}}{\sqrt{\sum\limits_{i}\left( {{AT}_{i} - {MT}_{i}} \right)^{2}} \cdot \sqrt{\sum\limits_{i}\left( {{ATA}_{i} - {MT}_{i}} \right)^{2}}}};$${{RE} = \sqrt{\frac{\sum\limits_{i}\left( {{AT}_{i} - {MT}_{i}} \right)^{2}}{\sum\limits_{i}{MT}_{i}^{2}}}};$${{RTS} = \frac{T_{s} - T_{I}}{T_{s}}};$

where AT_(i) is the activation time of grid point i in the imagedactivation sequence whereas MT_(i) is the measured activation time atthe identical position from the measured activation map. T_(s) is thesimulated or measured total activation time and T_(l) is the Imagedactivation total time. Localization Error is defined as the spatialdistance between the imaged activation initiation and the pacing site insimulation and animal study.

The Weighted Minimum Norm (WMN) method has been used in the previous 3Dcardiac electric imaging studies and has shown to have a generally goodperformance in imaging accuracy among the minimum norm based methods.Therefore, the performance of the CESI method was evaluated as comparedwith the WMN method. In all computer simulation and animal experiments,both CESI and WMN methods were performed independently and the resultsfrom both of the approaches were compared.

Results

A. Computer Simulations

Twelve different pacing sites were used in the single pacing paradigm.For each pacing site, various levels of Gaussian white noise were addedto the computed BSPM to simulate noise-contaminated measurements. Thestatistics of averaged CC, RE, LE and RTS on 12 pacing sites aresummarized in FIG. 4 to show the averaged statistics of LE (top left),CC (top right), RE (bottom left), and RTS (bottom right). Also, Table 1provides, as follows:

WMN CESI CC 0.83 ± 0.05 0.91 ± 0.03 RE 0.26 ± 0.05 0.15 ± 0.02 LE (mm) 7 ± 1.4  4 ± 1.4 RTS 0.21 ± 0.08  0.02 ± 0.004

The standard deviations of Gaussian white noise added to the BSPMs were0, 5 10, 20, 40, 60, 80 μV, respectively. Results in FIG. 4 and Table 1show that CESI has demonstrated a general improvement over WMN in allfour statistics. The imaging accuracy such as CC, RE and LE degradesslower than WMN while the noise level goes up and CESI can stillmaintain CCs as high as 0.92 and 0.94 even under the noise level as highas 60 and 80 μV. As for RTS, CESI was barely affected by the noise andmaintains the temporal resolution under each of the noisy circumstances.Dual site pacing simulations were also performed to evaluate the CESImethod and the statistics are summarized in Table 2, as follows:

20 μV Gaussian White Noise Hospital Recorded Noise WMN CESI WMN CESI CC0.85 ± 0.08 0.89 ± 0.07 0.80 ± 0.07 0.89 ± 0.07 RE 0.25 ± 0.06 0.12 ±0.06 0.30 ± 0.05 0.14 ± 0.08 LE (mm) 4.2 ± 2.1 3.9 ± 2.0 5.6 ± 3.2 4.1 ±1.7 RTS  0.2 ± 0.03  0.02 ± 0.004 0.25 ± 0.06  0.02 ± 0.005

Also, FIGS. 5A-5D present examples of single and dual site pacingcomputer simulation. All figures are color coded from early activation500 to late activation 502. For each activation sequence, the color codeis adapted to the length of the activation and marked in the color bar.Simulated activation sequences are presented in the first row of eachpanel in the figure. The generated BSPMs were contaminated withrealistic noise recorded from the hospital setting filtered with a 1-30Hz band pass FIR filter. The results from both approaches (CESI and WMN)are shown in the middle and the bottom row in each panel. FIGS. 5A-5Cshow single site pacing simulations on the LV basal anterior wall (FIG.5A), basal posterior wall (FIG. 5B), and RV free wall (FIG. 5C), whileFIG. 5D shows an example of dual site pacing simulation on the RV freewall and apical septum. CESI imaged activation sequences only showed aminimal loss of temporal resolution (˜1 ms) and demonstrated betteraccuracy on the general propagation pattern, in comparison to the delayof WMN estimated initial activation. For single pacing sites, CESIresults demonstrated higher concordance to the simulated results andsuffered less of a blurring effect compared with the WMN results. Theblurring effect shown in the WMN solutions in the figures is mostsignificant at the earliest and the latest period of activation,indicating a non-linear distortion on imaged activation time which canbe observed to be much relieved in CESI results. It can be seen fromFIGS. 5A-5D that CESI can image the early activation region clearly andthe initiation is shown to be in good agreement with the simulatedactivation pattern. The propagation pathway is also well depicted bothon the myocardial walls, close to epicardial surface, and the deepregion inside the heart along the septum. The termination of the beatwas also localized correctly, only with minor differences in the lateactivation pattern. In FIG. 5D, the dual site pacing simulation, thecontrast of CESI imaged activation to distinguish two pacing sites issignificantly higher than WMN results. The two pacing sites can beclearly identified from the CESI imaged results and the propagationpattern is in better agreement with the simulated pattern than WMNresults. The activation pattern in the myocardium around the two pacingsites is better imaged as a result of temporal resolution preservation.Both the pacing sites were imaged to be initiated independently at 0 ms,at the very beginning of the beat without interfering each otherregardless of their differences in location. The activation patternbetween the pacing sites is also well imaged whereas that in WMN resultis smeared due to the loss of temporal resolution. The statistics ofsimulation results with hospital recorded noise are summarized in Table1 (single site pacing) and Table 2 (dual site pacing).

To evaluate the robustness of the CESI method, various modeling errorsand co-registration errors were also simulated with 20 μV Gaussian whitesensor noise. In FIGS. 6A-6E, examples of imaging results from a pacingsimulation with various kinds of modeling and co-registration error areshown. All of the activation sequences are color coded from earlyactivation 600 to late activation 602 as marked in color bars. FIG. 6Apresents the computer simulated activation sequence. FIGS. 6B-6E displaythe imaging results and the comparisons of both CESI and WMN methodsunder various erroneous circumstances. FIG. 6B shows the results withtorso geometry uncertainty where torso geometry is 10% dilated. FIG. 6Cshows the results with heart position uncertainty where the wholemyocardium is moved 4 mm towards the left lung. FIG. 6D shows asituation in which both errors in FIGS. 6B and 6C occur together. FIG.6E shows the results with electrode-torso co-registration error whereall of the electrodes are 10 mm upward.

The imaged results showed that the CESI method maintains the temporalresolution (shrinkage ˜1 ms) and the activation pattern was barelyaffected by the modeling error or co-registration error. The CESI methodmaintains a stable overall pattern against modeling errors and littledistortion was observed. The initiations of the beats are well localizedby the CESI method with a clearly depicted early activation pattern. InFIGS. 6D, and 6E, where relatively heavy disturbance is imposed, theCESI method can still image the activation pattern with good accuracy.On the other hand, the WMN results, due to its physical constraints, areheavily distorted and losing details in activation pattern. In the earlyactivation area in FIGS. 6B and 6D as well as the late activation inFIGS. 6D and 6E, the smearing effect is obvious due to theminimum-energy constraints that promote the smoothness. The statisticsof the simulations are summarized in FIG. 7, where error 1 was torsogeometry dilated 10%; error 2 was heart position moved 4 mm towards leftlung; and error 3 was body surface electrodes move 10 mm towards righthand. Thus, the CESI method is much less affected by the modeling andco-registration error than the WMN method. CC, RE and RTS weremaintained within a relatively small range under all those erroneousconditions while LE is increased due to the modeling and co-registrationerror but still lower than WMN.

B. Animal Results

Intra-cardiac transmural bipolar mapping has been established as aneffective approach to measure the electrical activity and as a suitableapproach to evaluate 3D cardiac imaging techniques. Referring to FIGS.8A and 8B, 10 single pacing sites were employed in the pacing paradigmwith simultaneous body surface and intra-cardiac mapping. Specifically,representative examples and statistics of the imaging results andcomparisons are shown in FIGS. 8A and 8B. More particularly, FIGS. 8Aand 8B present two imaging examples with single pacing at RV (8A) and LV(8B), respectively. The activation sequences are color-coded from earlyactivation 800 to late activation 802. The black star represents theearliest activation site in both the imaged and measured activationmaps. The focal pattern of the activation as well as its initiation hasbeen well captured by the proposed method. The initiation is close tothe pacing site and the early activation region is well focused andclear. The imaged activation that were acquired using the CESI methodhas good consistency with the measured results along the time course,from the early phase 600 to the end of the beat. The imaged resultsacquired using the CESI method, in comparison with those acquired usingthe WMN approach, are in higher temporal resolution with only littledistortion especially in estimating the initial activation in thetemporal domain. Statistics of quantitative evaluations and comparisonsbetween CESI and WMN are summarized in FIG. 9. It can be observed thatCC, RE, and LE are generally improved. The RTS acquired using the CESImethod remains at 0.02, showing that the CESI approach is able tomaintain high temporal resolution at experimental circumstances.

Therefore, a novel cardiac electrical imaging technique, referred toherein as cardiac electrical sparse imaging (CESI), has been inventedand evaluated with computer simulations and animal experiments. CESIemploys a novel 4D inverse problem formulation to exploit the temporalsparse property of cardiac electrical activity to preserve the temporalresolution and detailed activation information for improved accuracy androbustness. Computer simulations of both single and dual site pacinghave shown that the CESI technique has the capability to image cardiacelectrical activities with high spatiotemporal resolution and improvedperformance. CESI is able to image the activation sequence with higherCC and lower RE, LE, and RTS in comparison to conventional minimum normbased (WMN) methods, represented by WMN in the simulated pacingparadigms. In addition, imaging accuracy can be well maintained againstvarious types of modeling error, indicating robustness in realisticclinical environments. Experiments in two rabbits using simultaneousBSPM and 3D intra-cardiac mapping further validated the CESI techniquein a quantitative and realistic manner. Comparisons between CESI and WMNbased imaging results show that the proposed method is able tooutperform conventional minimum energy techniques both in theoreticaland experimental evaluation. Results from both computer simulation andanimal experiments show that the proposed CESI method is in goodagreement with simulated activation sequence and experimentally measuredcardiac activation.

Efforts have been made in pursuit for high resolution noninvasiveimaging of cardiac electrical activity. The 4D inverse problemformulation in the CESI technique can image the whole cardiac electricalprocess and the weighted sparse constraints incorporate the temporalsparse property of cardiac electrical dynamics into reconstruction. Inthis invention a sparse problem formulation has been extended in amanner that is specifically designed and capable of imaging cardiacelectrical activation with dipole based temporal weighted constraintsand, thus, can reflect the electrophysiological dynamics. As explainedabove, the cardiac electrical activity can be approached as a sparseproperty. As explained herein, the temporal sparse property of cardiacelectrical dynamics can be derived directly from electrophysiologicalknowledge of myocardial cellular depolarization. In the presentinvention, cellular cardiac electrophysiological property as guidinginformation is incorporated into the reconstructing mathematicalframework of a physical model based 3D cardiac electrical imagingapproach as temporal constraints. The property is based on a phenomenonthat is not only observed in healthy but also in many pathologicalconditions. Moreover, this property is different from anelectrophysiological model that requires certain individualizedphysiological knowledge which can vary as the condition changes. Theinverse reconstruction of CESI employs a physical-model based strategy,but incorporates general physiological knowledge. The cardiac electricalinverse problem, by its nature, is often heavily ill-posed and thus notall the information can be directly reconstructed from the measurements.By incorporating the BSPM time course as input and temporal sparseconstraints to pinpoint the activation time, CESI is able to greatlydecrease the severity of ill-posedness and allow for a betterrepresentation of the information reflected in BSPM. The resolution of1.5 mm spatially and 1 ms temporal can be achieved. Unlike the energybased physical constraints such as minimum norm and singular valuetruncation, sparse constrained solution attempts to not omit thedetailed information in the solutions but to utilize the sparse propertyof the cardiac electrical activity for its reconstruction. With theseconstraints, the reconstruction algorithm will search for the solutionthat can fit the measurements well and at the same time has anelectrophysiologically based sparse property that will help prevent theloss of detailed information. Also, as can be found in the problemformulation, CESI defines a constrained convex problem and has a uniquesolution that can be obtained equivalently with different optimizationmethods. The reconstruction strategy in CESI seeks for a balance betweenthe physical model based techniques and their physiological model basedcounterparts. The experimental results described above demonstrate thatCESI is capable of imaging the electrical activation in the myocardiummore accurately and robustly than other methods, such as WMN, while atthe same time working without any individual- based physiologicalinformation.

CESI incorporates raw data from various modalities to image theelectrical activation in the 3D myocardium. In clinical practice, thequality of the raw data is limited. In the above-described results,various disturbances were simulated and tested with CESI. Compared tothe simulated white noise, the hospital recorded noise allows to examinethe performance of the imaging technique in a more realistic condition.The simulations with both generated white noise and hospital recordedsensor noise show that CESI was capable of imaging the electricalactivation in the myocardium with higher accuracy than WMN methods. CESIwas able to image with a CC=0.92, RE=0.15, LE=7 mm and RTS=0.02 underthe white noise disturbance as strong as 80 μV. In the simulationsutilizing the hospital recorded noise, CESI obtained a CC as high as0.91, RE, LE and RTS were controlled as low as 0.16, 3.8 mm and 0.02,respectively. The results demonstrate that CESI is capable of producingstable and accurate imaging results in relatively realistic conditions.In addition to sensor noise, imaging results with various modelingerrors that could occur in clinical conditions also demonstrate therobustness of CESI technique. Over the 4 kinds of modeling errors, thepresent method maintained a CC of 0.93, RE of 0.12, LE of 0.63 mm andRTS of 0.017, respectively. By comparing the modeling error results andthe modeling error free statistics shown in FIG. 4, one can find thatCESI has a strong robustness against the modeling errors and demonstratethe capability of functioning in complicated circumstances where thequality, and accuracy of raw data may be limited. For physical modelbased methods without physiological constraints, electrical energydistribution is heavily dependent by the accurate forward problemmodeling, so with erroneous modeling the imaging accuracy willdegenerate severely by the smearing and smoothing effect introduced. Incontrast, the sparse constraints used in CESI provide an underlyingpropagation mechanism as additional information for imaging andtherefore can prevent the activation sequence from server smoothing anddistorting effects.

Rigorous evaluation in biological systems is crucial for the assessmentof an imaging technique. Simultaneous recording of BSPM andintra-cardiac electrograms have been demonstrated as an effectiveapproach to evaluate the performance of non-invasive imaging techniquesin a realistic condition. The post-experiment CT scan can providedetailed information on the spatial location of intracardiac electrodesand therefore the electrical activity of the entire myocardium can bemapped over the 3D space. The results described above show that CESI canimage the cardiac activation sequences in good concordance with themeasured activation sequence via intracardiac mapping. The imagedactivation initiation sites lie close to the measured initiation sitesand the early activation area was clearly imaged. The animal experimentcan evaluate the method in a condition that is similar to clinicalpractice but still have direct measurements on the electrical activitythroughout the myocardial volume. As shown in FIG. 8, CESI can image thepaced beat with good accuracy and localization of the initiation andtherefore is expected to function with similar performance in realisticclinical conditions on focal arrhythmias. The comparisons between CESIand WMN show that the CESI imaged results suffer less distortion inactivation time (averaged CC>0.8, RE<0.2, LE˜5 mm) and can maintaintemporal resolution (RTS<0.02). The animal experiment resultsdemonstrate that CESI can be used to image the cardiac activationsequences in good concordance with intra-cardiac mapping.

In the clinical management of focal arrhythmias, such as prematureventricular complex and automatic ventricular tachycardia, catheterablation is usually performed on the suspected initiations of theectopic beats to terminate the arrhythmias. Therefore, the capability tocorrectly image the activation patterns in early phase of the ectopicbeat is of clinical importance. As shown in FIGS. 5A-5D, the presentmethod outperformed traditional minimum energy based method especiallyin early activation, identifying a clear initiation site and evading thesmearing effect that the (weighted) minimum norm methods usually imposeon the results and also leading a more accurate localization of ectopicinitiations with error around 4 mm. The animal experiments, compared tocomputer simulation, demonstrate the potential clinical performance ofCESI from a more realistic scope. Results show that CESI can localizethe pacing sites, which can generate an ectopic pattern similar to focalarrhythmias, within 5 mm. Noting that this error is generated by anintrinsic reconstruction strategy, CESI can localize the ablation targetwithin a smaller area and shorten the time of invasive mapping andablation.

CESI promotes sparse electrical activities in the temporal domain inorder to improve temporal resolution and accuracy of imaging. However,the method does not constrain the cardiac current density of “fire onlyonce”. The temporal sparse constraints seek to solve the inverse problemwith the most zeros, while at the same time staying in good compliancewith the residual term, which contains the information from BSPM.Therefore, multiple activation can coexist in the time course. Themethod is also compatible with non-focal arrhythmic activities, such asreentrant tachycardia.

As described, the above-detailed systems and methods may leverageinformation from non-interventional data acquisitions, such as ECGsystems using surface electrodes to thereby create BSPMs. However, theabove-described systems and methods may also use intracardiacelectrophysiological recordings or interventional data acquisitionssystems that include at least one electrode that interventionallypositioned, generally, using a cardiac catheter. For example, systemsand methods, such as described in U.S. Pat. No. 7,841,986, which isincorporated herein by reference in its entirety, may be used with thesystems and methods of the present invention. For example, referring nowto FIG. 10, the system described with respect to FIG. 1 may be adaptedto incorporate an intracardiac monitoring system 100. In this case, theintracardiac monitoring system 100 may be used instead of the ECG system13 and the use of ECG recordings 14 to produce body surface ECG data 18.Rather, the intracardiac monitoring system 100 can provide intracardiacmeasurements 102 that can be used create catheter based maps/images 104,as described in U.S. Pat. No. 7,841,986. The catheter based maps/images104 can then be used by the processor 32 to create activation images 24.While the use of the intracardiac monitoring system 100 and catheterbased maps/images may be an alternative to the ECG system 13 and theprocessing associated therewith, one may use both BSPM 22 andintracardiac catheter based maps/images 104 to perform cardiacactivation imaging. The combination of both data sources may provideenhanced performance.

In conclusion, cardiac electrical sparse imaging (CESI) systems andmethods are provided. These systems and methods have been evaluated witha series of computer simulations and animal pacing experiments. Thesimulation and animal results have demonstrated that CESI can image thecardiac electrical activation accurately and better than traditionallinear inverse methods in various conditions and in a realisticexperimental setup. The performance of CESI illustrates the ability tomap cardiac electrical activity and aid catheter ablation of arrhythmiain a clinical setting.

All references included herein are incorporated herein by reference intheir entirety. The present invention has been described in terms of oneor more preferred embodiments, and it should be appreciated that manyequivalents, alternatives, variations, and modifications, aside fromthose expressly stated, are possible and within the scope of theinvention.

1. A system for cardiac activation imaging, the system comprising: atleast one data acquisition device configured to acquire data about anelectrical activation of a heart of a subject; and a processorconfigured to receive the data acquired by the at least one dataacquisition device and generate a cardiac electrical activation image byreconstructing an activation image of the heart of the subject using aweighted sparse constrained reconstruction.
 2. The system of claim 1wherein the weighted sparse constrained reconstruction includes adipole-wise temporal weighted sparse reconstruction applied as:${\hat{J}}_{T} = {{{argmin}\left( {{{\overset{\rightarrow}{J}}_{T} - {L_{T}{\overset{\rightarrow}{\Phi}}_{T}}}}_{2}^{2} \right)}\mspace{14mu} {and}}$${{s.j.{\overset{T}{\sum\limits_{t}}{W_{t,i}{{\overset{\rightarrow}{J}}_{t,i}}_{2}^{1}}}} < {\mu \; E_{i}\mspace{14mu} {for}\mspace{14mu} {all}\mspace{14mu} i}};$where L_(T) stands for a transfer matrix connecting the data over aperiod of time, Φ_(T), and an equivalent current density (ECD) J_(T);W_(t,i) represents soft temporal weights of time instant t at locationgrid point i; E_(i) represents estimated energy of ECD along time courset at location i; and W_(t,i) and E_(i) can be derived by:${W_{t,i} = {{{\exp \left( {{- C_{t,i}}/C_{{ma}\; x}} \right)}\mspace{14mu} {and}\mspace{14mu} E_{i}} = \sqrt{\sum\limits_{T}C_{t,i}^{2}}}};$where C_(t,i) is soft-guiding information that can be solved withframe-by-frame minimum energy based inverse methods and μ is determinedby a regularization algorithm.
 3. The system of claim 1 wherein theprocessor is further configured to apply an image reconstructionframework that incorporates a cardiac electrophysiological property intoa physical-model based cardiac electrical imaging approach as temporalconstraints.
 4. The system of claim 3 wherein the physical-model basedcardiac electrical imaging approach is a three-dimensional (3D)physical-model based cardiac electrical imaging approach.
 5. The systemof claim 1 further comprising a display configured to provide theactivation image in a color coding along a continuum from earlyactivation to late activation.
 6. The system of claim 1 wherein theprocessor is configured to receive body surface ECG time coursesmeasured by body surface electrodes as an input and use the body surfaceECG time courses as a temporal sparse constraints in the weighted sparseconstrained reconstruction to identify cardiac activation sequence. 7.The system of claim 1 wherein the processor is configured to receivebody surface MCG time courses measured by MCG sensors out of the body asan input and use the MCG time courses as a temporal sparse constraintsin the weighted sparse constrained reconstruction to identify cardiacactivation sequence.
 8. The system of claim 1 wherein the processor isconfigured to balance fit with the data acquired and loss of detailedinformation.
 9. The system of claim 8 wherein the weighted sparseconstrained reconstruction includes an electrophysiologically basedsparse property that protects against loss of detailed information fromthe data acquired.
 10. The system of claim 9 wherein theelectrophysiologically based sparse property is a temporal sparseproperty of cardiac electrical dynamics derived directly fromelectrophysiological knowledge of myocardial cellular depolarization.11. The system of claim 1 wherein the at least one data acquisitiondevice includes one of an electrocardiography (ECG) device or aninterventional cardiac monitoring device such as a cardiac catheter. 12.A method for cardiac activation imaging, the method comprising:acquiring data about an electrical activation of a heart of a subjectusing at least one sensor; reconstructing an activation image of theheart of the subject using the acquired data and a weighted sparseconstrained reconstruction; and displaying the activation image of theheart.
 13. The method of claim 12 wherein the weighted sparseconstrained reconstruction includes a dipole-wise temporal weightedsparse reconstruction.
 14. The method of claim 13 wherein thedipole-wise temporal weighted sparse reconstruction is applied as:${\hat{J}}_{T} = {{{argmin}\left( {{{\overset{\rightarrow}{J}}_{T} - {L_{T}\overset{\rightarrow}{\Phi}}}}_{2}^{2} \right)}\mspace{14mu} {and}}$${{s.j.{\overset{T}{\sum\limits_{t}}{W_{t,i}{{\overset{\rightarrow}{J}}_{t,i}}_{2}^{1}}}} < {\mu \; E_{i}\mspace{14mu} {for}\mspace{14mu} {all}\mspace{14mu} i}};$where L_(T) stands for a transfer matrix connecting the data over aperiod of time, Φ_(T), and an equivalent current density (ECD) J_(T);W_(t,i) represents soft temporal weights of time instant t at locationgrid point i; E_(i) represents estimated energy of ECD along time courset at location i; and W_(t,i) and E_(i) can be derived by:${W_{t,i} = {{{\exp \left( {{- C_{t,i}}/C_{{ma}\; x}} \right)}\mspace{14mu} {and}\mspace{14mu} E_{i}} = \sqrt{\sum\limits_{T}C_{t,i}^{2}}}};$where C_(t,i) is soft-guiding information that can be solved withframe-by-frame minimum energy based inverse methods and,u is determinedby a regularization algorithm.
 15. The method of claim 12 wherein theweighted sparse constrained reconstruction applies an imagereconstruction framework that incorporates a cardiacelectrophysiological property into a physical-model based cardiacelectrical imaging approach as temporal constraints
 16. The method ofclaim 15 wherein the cardiac electrophysiological property is a temporalsparse property of cardiac electrical dynamics derived directly fromelectrophysiological knowledge of myocardial cellular depolarization.17. The method of claim 15 wherein the physical-model based cardiacelectrical imaging approach is a three-dimensional (3D) physical-modelbased cardiac electrical imaging approach.
 18. The method of claim 12further comprising receiving body surface ECG time course data measuredby body surface electrodes and using the body surface ECG time coursedata as a temporal sparse constraints in the weighted sparse constrainedreconstruction to identify cardiac activation time.
 19. The method ofclaim 12 further comprising receiving MCG time course data measured byMCG sensors and using the MCG time course data as a temporal sparseconstraints in the weighted sparse constrained reconstruction toidentify cardiac activation time.
 20. The method of claim 12 wherein theweighted sparse constrained reconstruction includes anelectrophysiologically based sparse property that protects against lossof detailed information from the acquired data.
 21. The method of claim20 wherein the electrophysiologically based sparse property is atemporal sparse property of cardiac electrical dynamics derived directlyfrom electrophysiological knowledge of myocardial cellulardepolarization.
 22. The method of claim 12 wherein the acquired dataincludes at least one an electrocardiography (ECG) acquired usingsurface electrodes or an interventional electrode such as a cardiaccatheter.
 23. The method of claim 12 wherein reconstructing includesdefining a constrained convex problem that has a unique solution.